A Single Server Queueing Loss Model with Heterogeneous Arrival and
Service
A heterogeneous arrival and service single server queueing loss model is
analyzed. The arrival process of customers is assumed to be a nonstationary
Poisson process with an intensity function whose evolution is governed by a
two-state continuous time Markov chain. Different service distributions for
different types of customers are allowed. The explicit loss formula for the
model considered is obtained. In a special case, it is shown that as the
arrival process becomes more regular the loss decreases. For single server loss
systems with renewal arrivals, counterexamples are given to show that
regularity of arrival and service distributions do not work to good effect in
general. Two sufficient conditions for it to be true are given.